The Future of Mathematics
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Opinion — commentary, not a factual news event.
AI can now crank out some math papers that used to look solid. The real fight is over who gets to do the thinking, not just the proving.
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Mathematicians are having an identity crisis, but not the melodramatic kind. In a recent post, Jeremy Avigad says the last few months of AI progress have changed everyday mathematical work enough that results that once seemed publishable can now be generated with a machine. The question isn’t whether mathematics survives. It’s what counts as doing mathematics when AI can handle more of the routine grind.
Avigad’s answer starts with scale. Today’s foundation models have seen the mathematical literature, and they’re tireless. Give them a swarm of agents and enough attempts, and they can stitch together known techniques until something works. That helps explain why the AI-generated solutions people have seen so far tend to look familiar: useful, sometimes impressive, but not obviously the kind of leap that changes the subject.
He argues that the harder, more interesting problems still matter because mathematics has always been bigger than the checklist of things we can prove. The field is a culture of rigorous reasoning and communication, he writes, and that culture doesn’t vanish because AI can solve more of the standard exercises. It just makes it easier to drift away from understanding unless humans keep choosing problems for their depth, not just their solvability.
Avigad leans on history to make the case. Riemann’s 1853 lecture, which helped introduce the manifold and separate metric from topological properties, looked obscure at the time and later became foundational; the same pattern holds, in different ways, for Galois, Poincaré, and Grothendieck. Those shifts weren’t judged by a reinforcement-learning score. Their value emerged over time, through human judgment, and that’s exactly the point: AI can assist, but it can’t decide what deserves to matter.
So he wants mathematicians to do more than defend old workflows. He says they should work with proof assistants, neural networks, symbolic automation, and other new tools as part of the job, not as a side hustle for technicians. That matters for the next generation, too. Departments and journal boards are already scrambling, but his message is plain: mathematics is still needed, the profession has to adapt, and this is the moment to shape what comes next rather than pretend the ground hasn’t moved.
My take — AI-written commentary, not fact-checked reporting
This is the right argument, and the profession should say it louder: if AI can spit out decent proofs, then the badge of honor is no longer repetition, it’s judgment. The math world has spent years pretending that tool use is somehow less pure; that ritual looks a bit silly now. Open tools, proof assistants, and messy experimentation are where the interesting work is headed, whether the old gatekeepers like it or not.
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